Poisson Processes

Toshio Nakagawa ()
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Toshio Nakagawa: Aichi Institute of Technology

Chapter Chapter 2 in Stochastic Processes, 2011, pp 7-46 from Springer

Abstract: Abstract It is well-known that most units operating in a useful life period, and complex systems that consist of many kinds of components, fail normally due to random causes independently over the time interval. Then, it is said in technical terms of stochastic processes, that failures occur in a Poisson process that counts the number of failures through time. This is a natural modeling tool in reliability problems. Some reliability measures such as MTTF (Mean Time To Failure), availability, and failure rate are estimated statistically from life data and are in practical use under such modelings without much theoretical arguments. Furthermore, because a Poisson process has stationary and independent properties, it is much convenient for formulating stochastic models in mathematical reliability theory.

Keywords: Failure Rate; Exponential Distribution; Poisson Process; Failure Time; Interarrival Time (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-85729-274-2_2

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